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Finding the Third Proportional to 450,196 and 686,729

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Solution

The third proportional to 450,196 and 686,729 is: 1,047,536.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    450,196 : 686,729 = 686,729 : x
  2. Step 2: Convert to fraction form
    450,196/686,729 = 686,729/x
  3. Step 3: Cross multiply
    450,196x = 686,729 × 686,729
  4. Step 4: Simplify right side
    450,196x = 471,596,719,441
  5. Step 5: Solve for x
    x = 471,596,719,441/450,196
  6. Step 6: Final answer
    x = 1,047,536.45

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.